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y=sqrt(arctg(x/3))
The derivative of the function/ y=sqrt(arctg(x/3))

Derivative of y=sqrt(arctg(x/3))

Function f() - derivative -N order at the point
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The graph:

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The solution

You have entered [src] 
    _________
   /     /x\ 
  /  atan|-| 
\/       \3/
atan⁡(x3)\sqrt{\operatorname{atan}{\left(\frac{x}{3} \right)}} 
sqrt(atan(x/3))
The graph
02468-8-6-4-2-101002
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
           1            
------------------------
  /     2\     _________
  |    x |    /     /x\ 
6*|1 + --|*  /  atan|-| 
  \    9 / \/       \3/
16(x29+1)atan⁡(x3)\frac{1}{6 \left(\frac{x^{2}}{9} + 1\right) \sqrt{\operatorname{atan}{\left(\frac{x}{3} \right)}}}
Simplify
The second derivative [src] 
       /   3         \   
    -3*|------- + 4*x|   
       |    /x\      |   
       |atan|-|      |   
       \    \3/      /   
-------------------------
          2     _________
  /     2\     /     /x\ 
4*\9 + x / *  /  atan|-| 
            \/       \3/
−3(4x+3atan⁡(x3))4(x2+9)2atan⁡(x3)- \frac{3 \left(4 x + \frac{3}{\operatorname{atan}{\left(\frac{x}{3} \right)}}\right)}{4 \left(x^{2} + 9\right)^{2} \sqrt{\operatorname{atan}{\left(\frac{x}{3} \right)}}}
Simplify
The third derivative [src] 
  /                             2                    \
  |             27          32*x           36*x      |
3*|-8 + ----------------- + ------ + ----------------|
  |     /     2\     2/x\        2   /     2\     /x\|
  |     \9 + x /*atan |-|   9 + x    \9 + x /*atan|-||
  \                   \3/                         \3//
------------------------------------------------------
                        2     _________               
                /     2\     /     /x\                
              8*\9 + x / *  /  atan|-|                
                          \/       \3/
3(32x2x2+9+36x(x2+9)atan⁡(x3)−8+27(x2+9)atan⁡2(x3))8(x2+9)2atan⁡(x3)\frac{3 \left(\frac{32 x^{2}}{x^{2} + 9} + \frac{36 x}{\left(x^{2} + 9\right) \operatorname{atan}{\left(\frac{x}{3} \right)}} - 8 + \frac{27}{\left(x^{2} + 9\right) \operatorname{atan}^{2}{\left(\frac{x}{3} \right)}}\right)}{8 \left(x^{2} + 9\right)^{2} \sqrt{\operatorname{atan}{\left(\frac{x}{3} \right)}}}
Simplify
The graph
Derivative of y=sqrt(arctg(x/3))
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